Acoustic Noise Reduction of Switched Reluctance Motor Drives

Transcription

1 Middle-East Journal of Scientific Research 8 (6): , 11 ISSN IDOSI Publications, 11 Acoustic Noise Reduction of Switched Reluctance Motor Drives M. Divandari and M.M. Kabir Department of Enineerin, Islamic Azad University, Aliabad Katoul Branch, Golestan, Iran Abstract: This paper presents a simple and novel procedure for acoustic noise reduction in Switched Reluctance Motors (SRMs) drive. The main sources of acoustic noise in a SRM are the radial manetic force and torque ripple. To investiate the radial force, an analytical relationship between motor desins and drive parameters is required. Thus, in this method two mathematical methods for calculation of radial force and torque have been proposed. These nonlinear relations show that phase current is one of the important factors in the SRM drive parameters because radial force and torque is dependent on the square of current, directly. The aim of this paper is the reduction of torque ripple and radial force by optimizin current wave form via fuzzy loic control. The FL injects an additional current for each phase current in reions which torque reduces and radial force is not maximized. The presented drive has been simulated by MATLAB/SIMULINK for nonlinear model of the SRM. The simulation results show that the proposed drive will decrease maximum radial force and torque ripple but will keep the previous maximum torque. This drive has the advantaes such as: simple implementation on the every SRM drive without extra hardware, low cost, hih reliability and excellent performance at lon term due to more less vibration. Key words : Switched Reluctance Motor (SRM) radial force torque ripple acoustic noise Fuzzy Loic (FL) current waveform INTRODUCTION Switched Reluctance Motors (SRM) have a wide rane of applications in industries, mainly due to the special properties of this motor. Hih reliability, the hih ratio of torque to power, robust contracture, low cost, hih efficiency, hih torque in low speed are only a few advantaes in SRM. Because of the mentioned reasons, SRM has underone rapid development in hybrid vehicles, wheelchairs, aircrafts, starter/enerator systems, washin machines and other automotive applications [1-8]. The main disadvantae of the motor is that it produces hih torque ripples. Torque control is a difficult task since the switched reluctance motor is intentionally operated in deep manetic saturation to increase the output power density. Gobbi et al. introduced a fuzzy iterative technique to modulate the phase current profile to minimize the torque ripples. The experimental results indicated that the torque ripple was reduced to lie within 5% of the desired steady torque in dynamic operatin conditions [1]. Two improved Torque-Sharin Functions (TSF) for implementin Torque Ripple Minimization (TRM) control were presented in [9]. The proposed torquesharin functions are dependent on the turn-on anle, overlap anle and the expected torque. A enetic alorithm was used to optimize the turn-on anle and the overlap anle at various expected torque demands operatin under the proposed TRM control in order to maximize the speed rane and minimize the copper loss [9]. In another study, Lee et al. proposed a novel and simple nonlinear loical TSF for a SRM drive. Their scheme usin nonlinear TSF manipulates currents in two adjacent phases durin commutation, so that efficiency and torque ripple in a SRM drive can be considerably improved [1]. We know SRM torque ripple and radial force are the main roots of acoustic noise eneration. Noise sources in electric machines are broadly cateorized as manetic, mechanical, electronic and aerodynamic as far as the production of direct airborne noise is concerned, the acoustic noise measured around an SRM is found to be directly correlated to the radial vibration of the stator yoke due to the radial manetic force. Radial force produced by the manetic flux crossin the air ap in an approximate radial direction excites various mode shapes [11]. However, control of SRM radial force is rarely discussed in the existin literature. Lin and Yan in [1] proposed a scheme that produces a controlled radial force for a 1/8-pole SRM. In their scheme, mutual inductances between stator poles are included in the control model. The motor torque has been controlled by the conventional method, i.e., all poles in the conduction phase were enerized with the Correspondin Author: M.M. Kabir, Department of Enineerin, Islamic Azad University, Aliabad Katoul Branch, Golestan, Iran 118

2 Middle-East J. Sci. Res., 8 (6): , 11 same current to produce the desired torque. Two extra poles from the descendin-inductance phase were enerized to produce the desired radial force. Excitin the stator windin in the SRM with a constant voltae, will make radial force, lateral force, tanential force and torque. The current in the stator windins of the SRM could interact with the local manetic field to produce a force on the windins. This force could excite windin vibrations that would emit acoustic noise. The windin vibrations could also excite stator vibrations that would emit acoustic noise [13]. However, if the SRM is already built, the acoustic noise reduction can be done by the optimization of drive parameters. Also, the radial force is the function of the phase current and the rotor position. Obtainin nonlinear relations of the radial force with the phase current and the rotor position is very important and the non-linear radial force simulation is also a key point for vibration and acoustic noise study [14]. Radial force is dependent on the lenth of air ap, rotor position, rotor lenth and radius of rotor, square of phase current and number of turns in one phase of the machine. Also, sound power radiated by a SRM is the function of radial force square [15]. Review in the researches of a recent decade about of the acoustic noise reduction of SRM drive shows most of researchers worked on the torque ripple reduction while motor desin parameters and radial manetic force are effective at acoustic noise and SRM vibrations. In the paper, with keep of maximum torque, the torque ripple and the maximum radial force has been reduced. This optimization is done by the current waveforms correction via FL. This procedure is based on injection of compensation current in each phase usin fuzzy loic. MATHEMATICAL NONLINEAR MODEL OF SRM T θ ω ( ϕ j / θ).ω ( ϕ j / i j ).ω W c T j T l T e N J l L r Time Rotor position Speed Backward Electromotive Force (EMF) Incremental inductance of the j th phase Co-enery Torque of j th phase Load torque Electromanetic torque Number of phases Moment of inertia of the rotor Lenth of air ap Stack lenth of rotor The phase flux linkae and instantaneous torque are variable aainst position and current. Consequently, flux and voltae for each phase of SRM are: ϕ = L (i, θ ).i (1) j j j j d ϕ (i, θ) ϕ di ϕ j j j j j dθ V= Ri + = Ri j jj dt jj i dt θ dt j di ϕ j j = Ri + L. +. ω jj j dt θ Finally, the torque of SRM is : () W (,i,l,l ) i (,i,l,l )di c θ j r = ϕθ (3) j r W ( θ,i,l,l ) c j r T = j θ i = const j n T = T e j j= 1 (4) (5) To study radial force and acoustic noise of SRM drives system, we need first to setup a nonlinear model for the SRM and develop the SRM differential equations. All of the dynamic characteristics of the SRM may be found if iven sufficient knowlede of the flux linkae and torque for each phase [16]. Nomenclature ϕ j L j V j i j R j Flux linkae of the j th phase Inductance of the j th phase Voltae of the j th phase Current of the j th phase Resistance of the j th phase 119 The mathematical motion of the motor by the action of electromanetic torque and load torque is: dω T T = J + Bω (6) e l dt The equation of motion can be expressed as dθ = ω (7) dt Accordin to these equations and experimentally measured characteristics, the representation of dynamic

3 Middle-East J. Sci. Res., 8 (6): , 11 Fi. 1: Representation of dynamic mathematical nonlinear model of 3-phase SRM mathematical non-linear model of SRM is illustrated as Fi. 1. CALCULATION OF SRM RADIAL FORCE As it was mentioned in previous sections, the radial force is dependent on the many parameters in the SRM and its drive. In the SRM, manetic radial force is based on the assumption of independent pole pairs. Manetic nonlinearity, machine eometry and material properties are all taken into account while calculatin the radial force. For more study on the radial force and acoustic noise both in the SRM desin and drive parameters, we need the fundamental equations and dimensions of SRM. Fi. illustrates the various dimensions involved in the derivation of radial, tanential and lateral forces. The air ap flux density at a iven stator and rotor pole overlap anle (θ), is iven as B(θ,i j,l,l r ) [15]. Then the followin variables are derived as: N.i ϕ ph j B ( θ,i,l,l) r = =µ.h =µ. j L r.r. θ l l ϕ N =. ph µ.l r.r.i θ j where r is the outer radius of the rotor, N ph is the number of turns in one phase of the machine, H is the manetic field strenth and µ is the permeability of air. The incremental electrical input enery (dw e ) is iven by: l ϕ dw = i.dλ= i.d(n.d ϕ ) = N.i.d ϕ=..dϕ (9) e j j ph ph j µ.l.r θ r The stored enery in the manetic field (W s ) is : (8) Fi. : Relevant dimensions of the SRM (radial, tanential and lateral forces) l.l.r. θ l r ϕ W =.B ( θ,i,l, L ) =. s µ j r µ.l.r θ r (1) where the term θ.l.l r ives the volume of the air ap contained by the stator and rotor pole overlap. Note that r.θ ives the arc of the overlappin reion between the stator and rotor poles. The enery balance equation nelectin losses is dw = dw + dw (11) e s m where dw m is the incremental mechanical enery and dw s is the incremental field enery. In this paper, to find the tanential, radial and lateral forces we present two methods. In the first method, to calculate the tanential force obtained from Eq. (1) as 1

4 Middle-East J. Sci. Res., 8 (6): , 11 l l ϕ ϕ dw =. d θ +. dϕ s µ.l.r.l.r r θ µ θ r (1) The second term on the riht side of Eq. (1) is due to the fact that ϕ is a function of the rotor position, lenth of air ap and current. Therefore, by substitutin Eqs. (9) and (1) in Eq. (11), the incremental mechanical enery is obtained as l ϕ dw =. dθ m µ.l.r r θ Consequently, electromanetic torque is obtained as: (13) where P s and P r are the number of stator and rotor poles, respectively. In the second method, to find the tanential, radial and lateral forces we will use Eq. (3) and flux equation. The flux equation is written as: µ.l.r. θ.n r ph ϕ= B ( θ, i, l,l ).A =.i j r l j µ.l.r. θ.n r ph =.ij l () Substitutin Eq. () in Eq. (3), co-enery is obtained as dw l l.r.l m ϕ r T = =. =.B ( θ,i,l,l ) e dθ µ.l.r j r r θ µ (14) µ.l.r. θ.n r ph W ( θ,i, l, L ) ==.i (1) c j r l j Also, the tanential force is obtained by dividin tanential torque by the radius of the rotor pole, yieldin: T l.l e r F = =.B ( θ,i,l,l ) t r µ j r and the radial force is iven by dw 1 r.l. m ϕ θ F = =. = r.b ( θ,i,l,l) n dl µ.r.l θ µ j r r Similarity, the lateral force can be derived as l.r. θ F =.B ( θ,i,l,l) y µ j r (15) (16) (17) The ratio of the radial force to the tanential force from Eqs. (16) and (15) becomes: F n r. θ = (18) F l t and rotor anle can be assumed to be the one phase conduction anle which in term of the rotor and stator poles is iven as Finally, torque and tanential, radial and lateral forces are obtained as W ( θ,i,l,l ) l c j r ϕ T = =. e θ µ.l.r r θ T l.l e r F = = K.( ) t r µ W ( θ,i,l, L ) c j r r.l. θ F = = K.( r ) n l µ W ( θ, i, l,l ) l.r. θ c j r F = = K.( ) y L µ r respectively. Where () (3) (4) (5) µ.n.i ph j K = (6) l Eqs. (), (4) and (6) show that the torque and the radial force have a direct dependent on the square of phase current. CALCULATION OF SRM ACOUSTIC NOISE 4. π θ (rad) = (19) P.P s r 11 The manitude of the acoustic noise at any operatin condition depends on the extent of

5 Middle-East J. Sci. Res., 8 (6): , 11 circumferential deflection due to the radial force wave (in N/m ), which is the radial force per unit operatin area. The analytical expression for the dynamic circumferential deflection for modes m can be expressed as [11]: where 1.F.R n(f ) m R exc.( m ) 3 m 4.E h D = s (7) circum(f ) exc f f {1 ( exc δ ) } + (. exc ) f π f m m n. ω.n rp f (n) = n.f = (8) exc p 6 ACOUSTIC NOISE REDUCTION VIA FUZZY LOGIC We know SRM torque ripple and radial force are the main reasons of acoustic noise eneration. Therefore, torque ripple and radial force minimization decrease mechanical stress, undesired effects on bearin and increase estimation precision in SRM drives []. In the SRM drive, radial force is dependent on L P D F K i ω circum n i Also, SRM torque is function of (31) T K i (3) e i Dcircum(f Amplitude of dynamic deflection (m); ) exc F n Amplitude of radial force wave (N/m ); δ Loarithmic decrement =.p dampin factor; N rp Number of rotor poles; ƒ p Fundamental frequency of phase current (Hz); ƒ exc (n) Excitation frequency (Hz) with n = 1,, 3, harmonic numbers; R m Mean radius of stator yoke; h s Stator pole heiht; m,ƒ m Circumferential mode number and mode frequency; E Module of stator material elasticity; Sound power radiated by an electric machine can be expressed as where P= 4σ ρcπ f D R l (9) 3 rel exc circum out stk P Radiated sound power (W); σ rel Relative sound intensity s rel =k /(1+k ); k Wave number k=(. p.r out. f exc )/c C Travelin speed of sound (m/s) in the medium; ρ.c 415 N.s/m 3 for air at C (ρ bein density of air; R out, l stk outer radius and stack lenth of the stator (m). Dependin on the threshold of human ear sensation, the reference of sound power level (P ref ) is 1-1 watt. Consequently, the acoustic noise power level in decibels becomes:.p L = 1lo( ) ω P ref (3) In the paper, we suppose SRM is already built. We want to optimize radial force and torque ripple in the SRM drive so far as keep maximum torque usin phase current waveform. Fiure 3 illustrates the characteristics of torque and radial force of SRM at rated current. Tow areas (A and B) can be seen in the fiure. In the A area not only torque decreases but also radial force increases and even will be maximized, but in the B area, torque increases and will be maximized, also radial force will not be maximized. In the proposed method, non-linear SRM torque characteristics are defined to A-G reions (Fi. 4). The width of each reion is five derees (while D reion width is fifteen derees) because in each reion, nonlinear torque behavior can be assumed to be linear. The SRM torque in the reions A, B, C increases and in the reion D almost is constant (and maximum also). In the reions E, F and G not only torque decreases but also radial force will be maximized. In the present work, FL acts on the phase current waveform to optimize torque ripple and maximum radial force. The A-G reions of SRM nonlinear torque have been shown in Table 1. Table 1: A-G Reions of SRM nonlinear torque Position (deree) θ<5 5 θ<1 1 θ<15 15 θ<3 3 θ<35 35 θ<4 4 θ<45 Reions A B C D E F G 1

6 Middle-East J. Sci. Res., 8 (6): , 11 Fi. 3: Characteristic of torque and radial force of SRM at rated current Fi. 6: Fuzzy loic member functions for current waveform Fi. 4: SRM nonlinear torque characteristics (A-G reions) Fi. 5: Block diaram of fuzzy loic for each phase The block diaram of Fuzzy Loic Control (FLC) for optimization of torque ripple and radial force for each phase has been shown in Fi. 5. FL acts on the reference current when θ<15 & 3 <θ 45 (A-C and E-G reions). Consequently, new reference current becomes: I = I + I (33) ref.new ref. Comp. Finally, Fi. 6 and Table show the fuzzy loic member functions for current waveform and fuzzy loic Table : Fuzzy loic rules CURRENT (A) NM NS Z PS PM NB PVB PVB PVB PB PB POSITION NM PVB PVB PB PB PM (DEGREE) NS PVB PB PB PM PS Z PB PB PM PS Z PS PB PM PS Z Z PM PM PS Z Z Z rules for acoustic noise reduction and torque ripple minimization, respectively. SIMULATION RESULTS The proposed method has been simulated by MATLAB /SIMULINK, where the parameters of SRM have been listed in the Table 3. Fiure 6-8 illustrates the simulation results without FLC. These results illustrate the one phase current, one phase radial force and total torque waveform, respectively. In these Fiures, the reference current and 13

7 Table 3: SRM Parameters Lmin Lmax = 8mH Minimum inductance = 6mH Maximum inductance β r= β s = 3 Middle-East J. Sci. Res., 8 (6): , 11 Rotor and stator pole anle = I. Hystersis band ω= 15rpm Rated speed V = 15v Rated voltae I = 1A Rated current Ns 6 Number of stator teeth N = 4 Number of rotor teeth r N = 3 Number of phases ph R = 1.3Ω Windin resistance Fi. 8: Total torque waveform of SRM without FLC Fi. 6: One phase current waveform of SRM without FLC Fi. 1: One phase current waveform of SRM with FLC Fi. 7: One phase radial force waveform of SRM without FLC the maximum radial force are 1A and N. Also, the maximum torque and the torque ripples are 3.5N.m and T = T max -T min = = (N.m), respectively. Fi. 11: One phase radial force waveform of SRM with FLC Finally, Fi. 1-1 illustrate the simulation results with FLC. These results show the one phase current, 14

8 Middle-East J. Sci. Res., 8 (6): , 11 Table 4: Simulation results Radial Ripple T (N.m) T m (N.m) force (N) percentae (%) With FLC Without FLC Difference reduced by the proposed method and current waveform optimization in the SRM drive decreases acoustic noise manitude, effectively. It can be obviously seen that the method has ood performance in lon rane. ACKNOWLEDGMENT This paper is supported by Islamic Azad University, Aliabad Katoul branch. Fi. 1: Total torque waveform of SRM with FLC one phase radial force and total torque waveform, respectively. In these Fiures, FLC optimizes reference current by means of reduction of maximum radial force and keepin the maximum torque and torque ripple minimization. It can be observed that the maximum radial force, the maximum torque and the torque ripple are N, 3.6N.m and T = T max -T min = = 1.35(N.m), respectively. Simulation results have been showed in the Table 4. CONCLUSIONS This study introduced a new phase current waveform by the 6/4 pole SRM were analyzed and simulated by means of acoustic noise reduction in the SRM drives. The hihest manitude of acoustic noise occurs when both radial force and torque ripple are maximized. Thus, two mathematical procedures for expressin the radial force and the torque have been described. Nonlinear relations show that one of the important factors in the drive parameters is current waveform manitude. In this paper, torque ripple and radial force have been reduced by deformation of the phase current waveform usin the fuzzy loic control. The control scheme is performed on the current profile while torque is lower than rated torque and radial force has been maximized. Simulation results demonstrated that the motor vibrations could be 15 REFERENCES 1. Gobbi, R., K. Ramar and N.C. Sahoo, 9. Fuzzy Iterative Technique for Torque Ripple Minimization in Switched Reluctance Motors. Electric Power Components and Systems, 37 (9): Divandari, M., R. Barzamini, A. Dadour and M. Jazaeri, 9. A Novel Dynamic Observer and Torque Ripple minimization via fuzzy loic for SRM Drives. IEEE International Conference, 1: Choi, Y.K., H.S. Yoon and C.S. Koh, 7. Pole- Shape Optimization of a Switched-Reluctance Motor for Torque Ripple Reduction. IEEE Transactions on Manetics, 43 (4): Ahn, J.W., S.J. Park and D.H. Lee, 4. Hybrid excitation of SRM for reduction of vibration and acoustic noise. IEEE Transactions on Industrial Electronics, 51 (): 4, Afjei, E., A. Seyadatan and H. Torkaman, 9. A New Two Phase Bidirectional Hybrid Switched Reluctance Motor/Field-Assisted Generator. Journal of Applied Sciences, 9 (4): Dursun, M., 8. A Wheelchair Driven with Fuzzy Loic Controlled Switched Reluctance Motor Supplied by PV Arrays. Journal of Applied Sciences, 8 (19): Torkaman, H. and E. Afjei, 6. Comprehensive Study of -D and 3-D Finite Element Analysis of a Switched Reluctance Motor. Journal of Applied Sciences, 8 (15): Venkatesan, G., R. Arumuam, S. Paramasivam, M. Vasudevan, and S. Vijayan, 6. Occurrence of Harmonics with Induction Machine and Switched Reluctance Machine: A Survey and Analysis. Journal of Applied Sciences, 6 (9): Xue, X.D., K.W.E. Chen and S.L. Ho, 9. Optimization and Evaluation of Torque-Sharin Functions for Torque Ripple Minimization in Switched Reluctance Motor Drives. IEEE Transactions on Power Electronics 4 (9): 76-9.

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